text: This cycle of excitation, polarization, depolarization, and re-polarization, etc. takes time before a net polarization is achieved. The buildup of nuclear polarization, P(t), is given by:
  Where ⟨P⟩ is the alkali metal polarization, γ is the spin exchange rate, and Γ is the longitudinal relaxation rate of the noble gas. Relaxation of the nuclear polarization can occur via several mechanisms and is written as a sum of these contributions:
  Where Γ, Γ, Γ, and Γ represent the relaxation from the transient Xe dimer, the persistent Xe dimer, diffusion through gradients in the applied magnetic field, and wall relaxation, respectively. In most cases, the largest contributors to the total relaxation are persistent dimers and wall relaxations. A Xe dimer can occur when two Xe atoms collide and are held together via van der Waals forces, and it can be broken when a third atom collides with it. It is similar to Xe-Rb during spin exchange (spin transfer) where they are held in close proximity to each other via van der Waals forces. Wall relaxation is when the hyperpolarized Xe collides with the walls of the cell and is de-polarized due to paramagnetic impurities in the glass.
  The buildup time constant, Γ, can be measured by collecting NMR spectra at time intervals falling within the time it takes to reach steady-state polarization (i.e. the maximum polarization that can be achieved, seen by the maximum signal output). The signal integrals are then plotted over time and can be fit to obtain the buildup time constant. Collecting a buildup curve at several different temperatures and plotting the values as a function of alkali metal vapor density (since vapor density increases with an increase in cell temperature) can be used to determine the spin destruction rate and the per-atom spin exchange rate using:
  Where γ is the per-atom spin exchange rate, [AM] is the alkali metal vapor density, and Γ is the spin destruction rate. This plot should be linear, where γ is the slope and Γ is the y-intercept.